Mean-field expansion for spin models with medium-range interactions

Abstract

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N )-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as R −3 , R being the range of the interactions. We compare our results with the existing numerical ones obtained by Monte Carlo simulations and present a critical discussion of other approaches.

Large- chiral transition in the Yukawa model

“…Quantitative results for the Yukawa model can be obtained by using the field-theoretical results of Refs. [10,13,12], or the Monte Carlo results available for medium-ranged models [18,19]. The necessary nonuniversal renormalization constants can be computed in perturbation theory.…”

“…[13] refers to correlations of the fields φ and not of the original fields ϕ. However, relation (4.12) of Ref.…”

“…An extensive discussion can be found in Refs. [10,13,9]. Let us first consider the standard φ 4 theory in d dimensions with d < 4.…”

“…For d = 3 the universal crossover curves have been computed in Refs. [10,11,13,12] (field theory) and in Ref. [19] (medium-range models).…”

“…One can use field theory and compute the crossover functions by resumming the perturbative series [10,11,12,13]. Alternatively, one can use the fact that the field-theoretical crossover is equivalent to the critical crossover that occurs in models with medium-range interactions [14,15,13,16,17]. This allows one to use the wealth of results available for these spin systems [14,18,19,15,13,17].…”